Answer:
θ = 5π/6, 7π/6
Explanation:
You want the solutions to 2cos(θ) = -√3 on the interval [0, 2π).
Cosine
The equation can be rearranged to ...
cos(θ) = -(√3)/2
By consulting your memorized short form table of trig function values, you know that the corresponding angles are 180°-30° and 180°+30°. In the range of interest, these angles in radian measure are ...
θ = 5π/6, 7π/6
In the attached figure, the cosine values are the x-coordinate of the point on the unit circle. The two points with x-coordinate -√3/2 are found on the left side at angles 150° and 210°.
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Additional comment
We like a graphing calculator for showing the solutions to equations like this. The third attachment shows the solutions are the values of x that satisfy ...
2cos(x) -(-√3) = 0
The zeros of the expression are the x-intercepts of its graph.